The present invention relates to a method and apparatus for the interferometric determination of the compressibility factor of a gas. More particularly, the invention is directed toward the precise determination of the compressibility factor from refractive index measurements.
The compressibility factor measures the deviation from the ideal gas law which describes the behavior of a perfect gas. A perfect gas assumes that there are no interactions between molecules. Although a perfect gas does not exist, most gases at low densities resemble closely the perfect gas. A perfect gas follows an ideal gas law given by EQU PV=nRT (1)
where P is the pressure, V is the volume, R is the universal gas constant, T is the absolute temperature and n is the number of moles. An ideal gas, however, is totally inadequate to describe the behavior of high-pressure gases. The ideal gas equation (1) can be modified to handle real gases by inserting the compressibility factor Z. Thus, the gas law can now be written as EQU PV=ZnRT (2)
The compressibility factor which must be determined from experiments is a function of temperature, pressure and gas composition. The precision in the measurement of the compressibility factor is important both from the point of view of fundamental as well as applied science. In molecular physics the compressibility factor is a direct measure of the importance of molecular interactions. In gas industry the compressibility factor is necessary to calculate the cost of natural gas. The cost of gas which depends on the heat content is calculated on the basis of heat per unit mass. The mass m of natural gas is derived from the compressibility factor by using the formula EQU m=MPV/ZRT (3)
where M is the molecular weight.
Until now, the most commonly used methods for the determination of the compressibility factor have been the Burnett expansion technique and constant or variable volume methods. In one commercial application of the Burnett mcthod, for example, the gas under test is contained at a measured pressure P.sub.1 above atmospheric pressure in one chambcr of volume V.sub.1 of a double chamber vessel which is in a constant temperature bath. The second chamber has a volume V.sub.2 usually at atmospheric pressure P.sub.2. The test gas is expanded to fill both chambers and the pressure P.sub.3 of the gas in the resultant volume V.sub.1 +V.sub.2 is measured. The compressibility factor Z.sub.1 is given by: ##EQU1## where K is the ratio V.sub.1 /V.sub.2, Z.sub.2 and Z.sub.3 are experimental values determined by iteration and represent respectively the compressibility factors at P.sub.2 and P.sub.3. Thus, the volume ratio K as well as the values of Z.sub.2 and Z.sub.3 must be determined experimentally. Although such a method enables one to determine the compressibility factor with a precision of about 0.01%, it is in general very time consuming particularly when use is made of a dead weight gauge to measure the pressure, in which case it may take several days to obtain a certain number of experimental values. Thus, only a limited number of experimental values can be obtained per unit of time with the Burnett method. The same applies with respcct to the constant or variable volume methods.